Planning our first vacation to San Diego for August. We are going with our 2 daughters (ages 16 and 13.) We don't plan on renting a car. We will be using taxis and trolleys to get around. But we do plan on going to the S.D. Zoo, Coronado Island, a Padres game, and Sea World. Did some research and we're not sure which section of S.D. is the best to stay. Should we stay downtown or in another part of S.D.? Really need your suggestions.

If you are not going to rent a car (and I urge you to reconsider)then your best bet is to stay in the downtown area, close to a Trolley station. You would be walking distance to Petco Park and a short cab ride from Balboa Park and the Zoo. You wouldn't be far from the Embarcadero with the Star of India and USS Midway.

Also, you could take the ferry to Coronado, then either walk or have a short cab ride to the other side of the "island" where the Hotel Del Coronado is situated, and the lovely beach.

Enjoy San Diego.

HI..
I'm with Barbara on the car thing.. You can do it but San Diego is a generally a car city.. Taxi's are not cheap and you can rent a compact/economy car for less than $20 a day at the airport. If you are still against the car, I would stay Downtown SD and you can go to all those places you listed via Trolley, Taxi and Water Taxi but it will probably be the same cost as renting a car and less hassle..
Holiday Inn at the Bay is a central location but there are a ton of Hotels downtown. Going to a Padre game, the Zoo, Coronado and SeaWorld are great places to see, especially since it's your first time and your kids will love it! The ocean temp is perfect in August and I am sure that the kids would love to boogie board in Coronado/La Jolla/Del Mar and it doesn't get any better than that!
I just checked Expedia 8/13-8/20 at the Sea Lodge Hotel in La Jolla right on the oceanfront for $219 a night..that is a deal and you and the kids would really get to see how beautiful SD is.. the water is very clean and perfect for snorkeling,kayaking, boogie boarding and it is central IF you rent a car! Usually the whole state of Texas takes over LJ Shores so I am surprised that they have it available.
www.ljbtc.com (to check out their website).
August is really busy so I would book as soon as you can and get the best rates whether it is direct or through Expedia, Priceline or Hotwire..
You really are going to have fun and have a blast!

A hotel downtown is the way to go. Thank you for your opinions/suggestions.

Any part of downtown San Diego, we should avoid?

Downtown is a pretty safe area. There aren't any hotels in areas I would want to avoid. Like any big city, bad things do occasionally happen.

as perviously mentioned, the holiday inn is a great location. if you want a place with a kitchen, check out embassy suites (although i'm not too certain how close to a trolley that is). if you have lots of money, there are some fancier ones right on the waterfront.